常利率下分红稀疏风险模型的期望折现罚金函数  

The Expected Discounted Penalty Function for a Thinning Risk Model with Constant Interest and Dividends

作　　者：赵金娥[1] 李明[1] 何树红[2] 

机构地区：[1]红河学院数学学院,云南蒙自661199 [2]云南大学数学与统计学院,云南昆明650091

出　　处：《郑州大学学报（理学版）》2015年第3期37-42,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号11301160;云南省科技厅自然科学研究基金资助项目;编号2013FZ116;云南省教育厅科研基金资助项目;编号2013C014;红河学院科研基金资助项目;编号XJ15SX06

摘　　要：考虑到保险公司的投资收益及分红策略,建立常利率和常数红利边界策略下的稀疏风险模型,其中保费收入不再是时间的线性函数,而是一个复合Poisson过程,且索赔次数是保单到达数的稀疏过程.利用全期望公式及盈余过程的强马氏性,得到了期望折现罚金函数、破产时的Laplace变换、破产时赤字的期望折现以及破产概率满足的积分微分方程,并借助合流超几何函数给出指数保费和指数索赔下破产概率的具体表达式.Considering the insurance company＇s investment income and dividend strategy,a thinning risk model was established. In contrast with the classical risk model where the premium process was a linear function of time,the aggregate premium process was a compound Poisson process and the claim number process was a thinning process of the premium arriving number process. Moreover,there were a constant interest and a constant dividend barrier strategy in this model. By taking full advantage of the total expectation formula and the strong Markov property of the surplus process,the integro-differential equations for the expectation discounted penalty function,the Laplace transform of the time of ruin,the discounted expectation of the deficit at ruin and the ruin probability were derived. Meanwhile,the explicit expression for the ruin probability was given in terms of the confluent hypergeometric functions when the individual stochastic premium amount and claim amount were exponentially distributed.

关 键 词：红利 常利率 期望折现罚金函数 破产概率 合流超几何函数 

分 类 号：O211.67[理学—概率论与数理统计]